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Properties

Label 60.240.18.v.1
Level $60$
Index $240$
Genus $18$
Analytic rank $5$
Cusps $6$
$\Q$-cusps $2$

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Invariants

Level: $60$ $\SL_2$-level: $60$ Newform level: $3600$
Index: $240$ $\PSL_2$-index:$240$
Genus: $18 = 1 + \frac{ 240 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 6 }{2}$
Cusps: $6$ (of which $2$ are rational) Cusp widths $20^{3}\cdot60^{3}$ Cusp orbits $1^{2}\cdot2^{2}$
Elliptic points: $0$ of order $2$ and $0$ of order $3$
Analytic rank: $5$
$\Q$-gonality: $4 \le \gamma \le 8$
$\overline{\Q}$-gonality: $4 \le \gamma \le 8$
Rational cusps: $2$
Rational CM points: none

Other labels

Cummins and Pauli (CP) label: 60G18
Rouse, Sutherland, and Zureick-Brown (RSZB) label: 60.240.18.28

Level structure

$\GL_2(\Z/60\Z)$-generators: $\begin{bmatrix}5&24\\18&5\end{bmatrix}$, $\begin{bmatrix}7&32\\9&53\end{bmatrix}$, $\begin{bmatrix}13&52\\9&7\end{bmatrix}$, $\begin{bmatrix}37&46\\36&55\end{bmatrix}$, $\begin{bmatrix}59&40\\18&31\end{bmatrix}$
Contains $-I$: yes
Quadratic refinements: 60.480.18-60.v.1.1, 60.480.18-60.v.1.2, 60.480.18-60.v.1.3, 60.480.18-60.v.1.4, 60.480.18-60.v.1.5, 60.480.18-60.v.1.6, 60.480.18-60.v.1.7, 60.480.18-60.v.1.8, 60.480.18-60.v.1.9, 60.480.18-60.v.1.10, 60.480.18-60.v.1.11, 60.480.18-60.v.1.12, 60.480.18-60.v.1.13, 60.480.18-60.v.1.14, 60.480.18-60.v.1.15, 60.480.18-60.v.1.16, 120.480.18-60.v.1.1, 120.480.18-60.v.1.2, 120.480.18-60.v.1.3, 120.480.18-60.v.1.4, 120.480.18-60.v.1.5, 120.480.18-60.v.1.6, 120.480.18-60.v.1.7, 120.480.18-60.v.1.8, 120.480.18-60.v.1.9, 120.480.18-60.v.1.10, 120.480.18-60.v.1.11, 120.480.18-60.v.1.12, 120.480.18-60.v.1.13, 120.480.18-60.v.1.14, 120.480.18-60.v.1.15, 120.480.18-60.v.1.16, 120.480.18-60.v.1.17, 120.480.18-60.v.1.18, 120.480.18-60.v.1.19, 120.480.18-60.v.1.20, 120.480.18-60.v.1.21, 120.480.18-60.v.1.22, 120.480.18-60.v.1.23, 120.480.18-60.v.1.24, 120.480.18-60.v.1.25, 120.480.18-60.v.1.26, 120.480.18-60.v.1.27, 120.480.18-60.v.1.28, 120.480.18-60.v.1.29, 120.480.18-60.v.1.30, 120.480.18-60.v.1.31, 120.480.18-60.v.1.32, 120.480.18-60.v.1.33, 120.480.18-60.v.1.34, 120.480.18-60.v.1.35, 120.480.18-60.v.1.36, 120.480.18-60.v.1.37, 120.480.18-60.v.1.38, 120.480.18-60.v.1.39, 120.480.18-60.v.1.40, 120.480.18-60.v.1.41, 120.480.18-60.v.1.42, 120.480.18-60.v.1.43, 120.480.18-60.v.1.44, 120.480.18-60.v.1.45, 120.480.18-60.v.1.46, 120.480.18-60.v.1.47, 120.480.18-60.v.1.48
Cyclic 60-isogeny field degree: $12$
Cyclic 60-torsion field degree: $192$
Full 60-torsion field degree: $9216$

Jacobian

Conductor: $2^{41}\cdot3^{23}\cdot5^{34}$
Simple: no
Squarefree: no
Decomposition: $1^{18}$
Newforms: 48.2.a.a, 50.2.a.b$^{2}$, 75.2.a.a$^{2}$, 225.2.a.a, 400.2.a.a$^{2}$, 450.2.a.g$^{2}$, 900.2.a.c, 1200.2.a.j, 1200.2.a.q, 1800.2.a.a, 1800.2.a.m, 1800.2.a.r$^{2}$, 1800.2.a.t

Rational points

This modular curve has 2 rational cusps but no known non-cuspidal rational points.

Modular covers

This modular curve minimally covers the modular curves listed below.

Covered curve Level Index Degree Genus Rank Kernel decomposition
60.48.2.f.1 $60$ $5$ $5$ $2$ $1$ $1^{16}$
60.60.4.cj.1 $60$ $4$ $4$ $4$ $1$ $1^{14}$
60.120.9.dt.1 $60$ $2$ $2$ $9$ $2$ $1^{9}$

This modular curve is minimally covered by the modular curves in the database listed below.

Covering curve Level Index Degree Genus Rank Kernel decomposition
60.480.35.j.1 $60$ $2$ $2$ $35$ $9$ $1^{17}$
60.480.35.ce.1 $60$ $2$ $2$ $35$ $10$ $1^{17}$
60.480.35.ek.1 $60$ $2$ $2$ $35$ $11$ $1^{17}$
60.480.35.en.1 $60$ $2$ $2$ $35$ $14$ $1^{17}$
60.480.35.fj.1 $60$ $2$ $2$ $35$ $10$ $1^{17}$
60.480.35.fm.1 $60$ $2$ $2$ $35$ $12$ $1^{17}$
60.480.35.fr.1 $60$ $2$ $2$ $35$ $7$ $1^{17}$
60.480.35.fu.1 $60$ $2$ $2$ $35$ $9$ $1^{17}$
60.720.52.p.1 $60$ $3$ $3$ $52$ $15$ $1^{34}$
60.720.55.vt.1 $60$ $3$ $3$ $55$ $16$ $1^{37}$
60.960.69.si.1 $60$ $4$ $4$ $69$ $19$ $1^{51}$